IJPAM: Volume 101, No. 6 (2015)

TOTAL VERTEX IRREGULARITY
STRENGTH OF CIRCULAR LADDER
WINDMILL AND BOW GRAPHS

Indra Rajasingh$^1$, V. Annamma$^2$
$^1$School of Advanced Sciences
VIT
Chennai, 600 127, INDIA
$^{2}$Department of Mathematics
L.N. Govt. College
Ponneri, 601 204, INDIA


Abstract. Let $G(V,E)$ be a simple graph. For a labeling $\partial :V\cup E\rightarrow \{1,2,3,...,k\}$ the weight of a vertex $x$ is defined as $% wt(x)=\partial (x)+\underset{xy\in E}{\sum }\partial (xy).$ $\partial $ is called a vertex irregular total $k$-labeling if for every pair of distinct vertices $x$ and $y$ $wt(x)\neq wt(y)$. The minimum $k$ for which the graph $G$ has a vertex irregular total $k$-labeling is called the total vertex irregularity strength of $G$ and is denoted by $tvs(G).$ In this paper we determine the total vertex irregularity strength of circular ladder, windmill graph and uniform bow graph.

Received: March 12, 2015

AMS Subject Classification: 05C78

Key Words and Phrases: graph labeling, total vertex irregularity strength (tvs), weight of a vertex, circular ladder, windmill graph, uniform bow graph

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DOI: 10.12732/ijpam.v101i6.24 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 6
Pages: 1063 - 1078


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